Box: Using Chained-Dollar Estimates for Computing Contributions to Economic
Growth: A Cautionary Note

The Bureau of Economic Analysis (BEA) measures real output and prices using
chain-type annual-weighted indexes computed with a Fisher formula. These
measures, which were introduced in the most recent comprehensive revisions of
the national income and product accounts and of the gross product originating by
industry (GPO) estimates, allow for the effects of changes over time in relative
prices and quantities. By eliminating the substitution bias inherent in the
previously featured fixed-weighted measures of real output and prices, these new
indexes provide significantly more accurate measures of growth in real GDP and
other major economic aggregates./1/

As a convenience for data users, BEA also prepares dollar-denominated real
output series that are consistent with the chain-type indexes and that retain
some of the computational advantages of constant-dollar series. The real
chained (1992) dollar estimates for a GDP expenditure component or for a GPO
industry are derived as the product of the chain-type quantity index (divided by
100) and the corresponding 1992 current-dollar value. Because the formula for
the chain-type quantity indexes uses weights of more than one period, the
corresponding chained-dollar estimates are usually not additive.

For many analytical purposes, these chained-dollar estimates are appropriate
and informative. Growth rates and percent changes based on chained dollars are
always equivalent to those derived from the quantity indexes and can be used
confidently over any time period. Contributions to change computed from
published chained dollars are usually appropriate for periods close to the
reference year, especially for components or industries whose prices have not
changed substantially relative to GDP prices.

However, if relative prices for individual GDP expenditure components or for
GPO industries have changed substantially, then calculations of contributions to
economic growth based on published chained-dollar estimates may be misleading
and inappropriate even for short periods close to the reference year. Even for
highly aggregated expenditure categories or for industry groups, the
calculations will usually be misleading over long periods, because relative
prices are likely to change substantially./2/

The accompanying exhibit shows the contributions
of industry groups to the change in real GDP for 197782 based on chained
(1992) dollars and on chained (1977) dollars. (The period 197782 was
chosen for illustrative purposes because it is relatively far from the
reference year for published chained (1992) dollars.) Contributions to the
change in real GDP were computed by dividing the change in chained dollars for
an industry group by the change in chained dollars for GDP for the period. For
many industry groups, the contributions are very similar using either 1977 or
1992 as the reference year, but for some industry groups, they differ
substantially. As measured using chained (1992) dollars, services account for
37 percent of real GDP growth in 197782; as measured using chained (1977)
dollarsa more appropriate (contemporaneous) reference periodservices
account for 28 percent. Similarly, the contribution of finance, insurance, and
real estate (FIRE) is 39 percent based on chained (1992) dollars and 31 percent
based on chained (1977) dollars. These differences arise because the GPO prices
of services and of FIRE increased substantially relative to GDP prices from
1977 to 1992, whereas the GPO prices of most other industry groups declined
relative to GDP prices. Thus, using the relative prices of 1992 for services
and FIRE overstates their contribution to real economic growth in the earlier
period.

The contributions to real GDP growth computed from chained-dollar estimates
can be misleading not only for industry groups over long time periods, but also
for detailed industries during periods of rapid changes in relative prices, even
for periods that are relatively close to the chained-dollar reference year. To
illustrate, the contributions of detailed industries to the change in GDP for
1997 were computed using the published chained (1992) dollars and using an
alternative measure based on chained (1996) dollars. For most industries, the
alternative measure yields the same or similar estimates of contributions to
real GDP growth. However, for two industries for which GPO prices have
increased much slower relative to GDP pricesindustrial machinery and
equipment (which includes computers) and electronic and other electric
equipment (which includes semiconductors)the contributions are
substantially overstated using chained (1992) dollars: For industrial machinery
and equipment, 11.6 percent, compared with 8.6 percent using chained (1996)
dollars; and for electronic and other electric equipment, 17.5 percent, compared
with 10.6 percent. Conversely, the contribution of the insurance carriers
industry is somewhat understated2.1 percent, compared with 2.7 percentbecause
the GPO price for this industry increased much faster than GDP prices.

For analyses of contributions to the change in real GDP, BEA strongly
recommends the use of the published contribution-to- growth tables. Table 2 in
the monthly GDP news release and NIPA
table 8.2, which is on page D25
of this issue, provide accurate measures of the contributions of the major GDP
expenditure components to the percent change in real GDP for all periods; these
tables use exact formulas for attributing growth to the components of GDP.
Table 2 in this article provides estimates of annual
contributions to the percent change in real GDP for industry groups based on
approximations to the exact formula. The estimates for each year are based on
the prior year's current-dollar estimates, and the average annual contribution
for 199297 is computed as the average of the annual percentage-point
contributions.

For some analytical purposes, it may be desirable to compute contributions
to growth for more than a single period or for aggregates other than GDP. Users
can prepare close approximations of these contributions using chain-type
annual-weighted indexes. In effect, users compute a chained-dollar series for a
particular period using the percent changes in the chain-type annual-weighted
indexes to compute chained-dollar series indexed to the current dollars of the
reference period appropriate for the analysis (see footnote 1
for a reference to additional information on these calculations). Another
alternative is to use the same procedure as that used for table
2 in this article. In table 2, the contributions
of industry groups to real GDP growth for 1993 were computed by (1)
extrapolating the 1992 estimates of current-dollar GDP and GPO by the percent
changes in the corresponding GDP and GPO chain-type quantity indexes from 1992
to 1993, (2) calculating each industry group's percentage contribution to the
change in real GDP for 1993 based on chained dollars, and (3) multiplying these
percentages by the percent change in real GDP for 1993. The contributions for
1994 were computed by extrapolating the 1993 current-dollar estimates by the
percent changes in the chain-type quantity indexes from 1993 to 1994. These
estimates were then used to calculate the contribution of each industry group to
the change in real GDP for 1994 based on chained (1993) dollars. As with the
calculations for contributions to real GDP growth for 1993, these percentage
contributions to growth for 1994 were then multiplied by the percent change in
real GDP for 1994. This procedure was repeated to calculate each industry
group's percentage-point contribution to real GDP growth for each year (1993,
1994, 1995, 1996, and 1997). The average annual contribution for 199297
was then computed for each industry group as the simple average of each year's
percentage-point contribution.

2. Comparisons among the chained (1992) dollar estimates
of components or industries may be particularly misleading for periods before
1982. For example, during the World War II era, the share of GDP accounted for
by government consumption expenditures and gross investment increased
substantially, and prices throughout the economy were tightly controlled and
very different from postwar levels. These changes in the structure of the
economy, while relatively short lived, seriously affect computations of
contributions to GDP growth in this period.